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A fascinating memoir from the man who revitalized visual geometry, and whose ideas about fractals have changed how we look at both the natural world and the financial world.

Benoit Mandelbrot, the creator of fractal geometry, has significantly improved our understanding of, among other things, financial variability and erratic physical phenomena. In The Fractalist, Mandelbrot recounts the high points of his life with exuberance and an eloquent fluency, deepening our understanding of the evolution of his extraordinary mind. We begin with his early years: born in Warsaw in 1924 to a Lithuanian Jewish family, Mandelbrot moved with his family to Paris in the 1930s, where he was mentored by an eminent mathematician uncle. During World War II, as he stayed barely one step ahead of the Nazis until France was liberated, he studied geometry on his own and dreamed of using it to solve fresh, real-world problems. We observe his unusually broad education in Europe, and later at Caltech, Princeton, and MIT. We learn about his thirty-five-year affiliation with IBM’s Thomas J. Watson Research Center and his association with Harvard and Yale. An outsider to mainstream scientific research, he managed to do what others had thought impossible: develop a new geometry that combines revelatory beauty with a radical way of unfolding formerly hidden laws governing utter roughness, turbulence, and chaos.

Here is a remarkable story of both the man’s life and his unparalleled contributions to science, mathematics, and the arts.

Editorial Reviews

Amazon.com Review

Guest Reviewer: Nassim Nicholas Taleb

Nassim Nicholas Taleb, author of The Black Swan: The Impact of the Highly Improbable and Antifragile: Things That Gain from Disorder, has devoted his life to problems of uncertainty, probability, and knowledge. He spent nearly two decades as a businessman and quantitative trader before becoming a full-time philosophical essayist and academic researcher in 2006. Although he spends most of his time in the intense seclusion of his study, or as a flâneur meditating in cafés, he is currently Distinguished Professor of Risk Engineering at New York University’s Polytechnic Institute. His main subject matter is "decision making under opacity", that is, a map and a protocol on how we should live in a world we don't understand. Taleb's books have been published in thirty-three languages.

"I have never done anything like others", Mandelbrot once said. And indeed these memoirs show it. He really managed to do everything on his own terms. Everything. It was not easy for him, but he end up doing it as he wanted it.

Consider his huge insight about the world around us. "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line", wrote Benoit Mandelbrot, contradicting more than 2000 years of misconceptions. Triangles, squares, and circles seem to exist in our textbooks more than reality—and we didn't notice it. Thus was born fractal geometry, a general theory of "roughness". Mandelbrot uncovered simple rules used by nature (and men) that, thanks to repetition, by smaller parts that resemble the whole, generate these seemingly complex and chaotic patterns.

Self-taught and fiercely independent, he thought in images and passed the entrance exam of the top school of mathematics without solving equations; he was both precocious and a late bloomer producing the famous "Mandelbrot set" when he was in his fifties and got tenure at Yale when he was 75. Older mathematicians have resisted his geometric and intuitive method—but the top prize in mathematics was recently given for solving one of his sub-conjectures.

Mandelbrot, while a bit of a loner, had perhaps more cumulative influence than any other single scientist in history, with the only close second Isaac Newton. His contributions affected physics, engineering, arts, medicine (our vessels, lungs, and brains are fractal), biology, etc. But he was unheeded by the very field he started in, economics, where he proved in the 1960s that financial theories vastly underestimate market risk and need total revamping—in spite of the current crisis.

I met him when he was in his late seventies, as he was writing these memoirs long hand. He was the only teacher I ever had, the only person for whom I have had intellectual respect. But there was something else that made him magnetic: he was a raconteur with a profound sense of historical context ... Reading these memoirs put me back in the unusual atmosphere he created around him. The reader is made to feel he are at the center of twentieth century science as it was produced with fields invented almost from scratch: Max Delbrück with molecular biology, Paul Lévy with the mathematics of probability, Robert Oppenheimer with nuclear physics, even Jean Piaget the psychologist for whom Mandelbrot worked as a scientific assistant. And many more.

Finally, the reader will be presented with something that no longer exists in intellectual life: force of character and independence. Enjoy the book.

Review

“This is a wonderful memoir. It is personal, occasionally opinionated, at times beautifully written, and with a narrative encompassing a wide range of times, places, and people.” –Mark McCartney, London Mathematical Society

“Mandelbrot changed the way we look at a wide range of random phenomena from commodity prices to the shapes of mountains, rivers, and coastlines…The memoir captures the enthusiasm as well as the memories of a visionary who loved nothing better than studying complex multidisciplinary concepts.” –Publishers Weekly

“‘When I find myself in the company of scientists,’ W. H. Auden wrote, ‘I feel like a shabby curate who has strayed by mistake into a drawing room full of dukes.’ Benoit B. Mandelbrot (1924-2010) had the kind of beautiful, buzzing mind that made even gifted fellow scientists feel shabby around the edges…The Fractalist evokes the kinds of deceptively simple questions Mandelbrot asked—‘What shape is a mountain, a coastline, a river or a dividing line between two river watersheds?’—and the profound answers he supplied.” –Dwight Garner, The New York Times

“Memoir of a brilliant mathematician who never thought of himself as a mathematician…charmingly written.” –Kirkus

“Benoit Mandelbrot was the one who let us appreciate chaos in all its glory—the noisy, the wayward, and the freakish, from the very small to the very large. He invented a new and slightly nebulous field of study—a kind of geometry, for want of a better description—and he invented that recondite name for it, fractal. “Clouds are not spheres—the most famous sentence he ever wrote—mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. “They are all fractal. Clouds, mountains, coastlines, bark, and lightning: jagged and discontinuous, they are shapes that branch out or fold in upon themselves recursively. “He found relevant mathematics in some old and freakish ideas—‘monsters,’ as he said, ‘mathematical pathologies’ that had been relegated to the fringes. “‘I started looking in the trash cans of science for such phenomena,’ he said, and he meant this literally: one scrap he grabbed from a mathematician’s wastebasket to read on the Paris subway inspired an important 1965 paper, ‘Information Theory and Psycholinguistics.’ Information theory led to fractals when he took a close look at the problem of noise in communications lines. There was always noise, and on average it seemed manageable, but analysis revealed that normal bell-curve averages didn’t apply. “It was the same with brainwaves, fluid turbulence, seismic tremors, and—oh, yes—finance. “But he was not really an economist, or a physiologist, or a physicist, or an engineer. “‘Very often when I listen to the list of my previous jobs, I wonder if I exist,’ he said once. ‘The intersection of such sets is surely empty.’”—James Gleick, author of The Information

“The Fractalist is a well-written tale of a scientific life, complete with first-person accounts of a surprising range of scientific greats.” –Stephen Wolfram, The Wall Street Journal

Most Helpful Customer Reviews

"My life", says Benoit Mandelbrot in the introduction to his memoir, "reminds me of that fairy tale in which the hero finds a hitherto unseen thread, and as he unravels the thread it leads him to unimaginable and unknown wonders". Mandelbrot not only found those wonders, but bequeathed to us the thread which will continue to lead us to more wondrous discoveries.

Mandelbrot was one of those chosen few scientists in history who are generalists, people whose ideas impact a vast landscape of fields. A maverick in the best sense of the term, he even went one step further and created his own field of fractal geometry. In a nutshell, he developed a "theory of roughness", and the fractals which represent this roughness are now household names, even making it into "Jurassic Park". Today fractals are known to manifest themselves in a staggering range of phenomena; the rhythms of the heart, the distribution of galaxies, market fluctuations, the rise and fall of species populations, the shapes of blood vessels, earthquakes, and the weather. Before Mandelbrot scientists liked to deal with smooth averages and equilibria, assuming that the outliers, the "pathologies", the sudden jumps from normalcy were rare and could be ignored. Mandelbrot proved that they can't and found methods to tame them and bring them into the mainstream. His insights into this new view of nature effected minor and major revolutions in fields as diverse as economics, astronomy, physiology and fluid dynamics. More than almost any other thinker he was responsible for teaching natural and social scientists to model the world as it is rather than the abstraction which they want it to be.

In this memoir Mandelbrot describes his immensely eventful and somewhat haphazard journey to these revelations.Read more ›

I came to know Benoit Mandelbrot's work through the writings of Nassim Taleb, little did I know at the time "Mandelbrotian" would play a significant role in changing my life. The day the memoir came out, I finished the entire work and have since reread it again. I lack the words to describe how inspirational Mandelbrot's work is to followers of his fractal geometry, even if they are not professional mathematicians.

For people that have a fear of math - this is a great book. In fact, there is only one equation in the entire book. Instead this memoir gets into the thoughts of one of the 20th century's greatest minds. Mandelbrot constantly avoided structure, smoothness, and the status quo. In essence, his life was rough and that was exactly the way he liked it. Despite living under constant uncertainty, Mandelbrot never complains or worries over the lack of security he faced, frankly, he realized that he thrived under such conditions.

It was refreshing to read a memoir free of over-causation. Often the autobiography of a famous person is filled with causes on how and why they were so successful.. Instead, Mandelbrot writes the major events in his life as best he can remember them (often finding support in pictures or items from his archives) and examines how luck, skill, and perseverance shaped his career. Sometimes choices were made for him, other times he chose an unconventional path on purpose but he never stopped trying to find his "Keplerian" contribution to math. Somehow he grasped at a young age that true discoveries are not gained through climbing the established academic ladder but by tinkering on the verge of such structures.Read more ›

Like Sinatra, he did it his way. He crossed disciplines searching for a theory of roughness, sought after since antiquity, and he found it at age 55, in the Mandelbrot set, when most scientists, mathematicians, so on, have seen their best work done and gone. Hopping and skipping over the hot coals of academic demands that he stick to one subject, he chose to let his mind go where it would. Mandelbrot's memoir clears a bit of brush for the next maverick whether he or she be in geometry, molecular biology, or in any future, yet unrecognized discipline. "The Fractalist" is written with a youthful mind, looking forward, always.

Mandelbrot, inventor of fractal geometry, in his own words, perhaps lightly edited, wanted to tell an upcoming generation about the journey of an "outlier", who wanted to say that the rules can be broken, that a life of the mind is preferable in some to wealth, and that the pinnacle of success is reachable climbing this not often taken path.

The wild state: Mandelbrot tells us through a life story that education is no longer about who is worthy enough, as it was often in 1940's France when he came out of hiding after the war to prepare for entrance exams in a few month's time. It is about who is curious enough, whose mind is in one of the three states of risk and randomness, "mild, slow, or wild." Benoit Mandelbrot's mind was definitely in the "wild" state, full of heat and passion for connecting novel ideas.

Benoit Mandelbrot's writing charms, it wanders off, it shows that it's difficult even for a genius to write a coherent memoir, but don't let that stop you. The book has only one formula in it, and major concepts peppered throughout it, in introductory form mostly.Read more ›